Design hydrograph estimation in small and ungauged watersheds: continuous simulation method versus event‐based approach

The proper assessment of design hydrographs and their main properties (peak, volume and duration) in small and ungauged basins is a key point of many hydrological applications. In general, two types of methods can be used to evaluate the design hydrograph: one approach is based on the statistics of storm events, while the other relies on continuously simulating rainfall‐runoff time series. In the first class of methods, the design hydrograph is obtained by applying a rainfall‐runoff model to a design hyetograph that synthesises the storm event. In the second approach, the design hydrograph is quantified by analysing long synthetic runoff time series that are obtained by transforming synthetic rainfall sequences through a rainfall‐runoff model. These simulation‐based procedures overcome some of the unrealistic hypotheses which characterize the event‐based approaches. In this paper, a simulation experiment is carried out to examine the differences between the two types of methods in terms of the design hydrograph's peak, volume and duration. The results conclude that the continuous simulation methods are preferable because the event‐based approaches tend to underestimate the hydrograph's volume and duration. Copyright © 2011 John Wiley & Sons, Ltd.     

Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River

As an alternative to the commonly used univariate flood frequency analysis, copula frequency analysis can be used. In this study, 58 flood events at the Litija gauging station on the Sava River in Slovenia were analysed, selected based on annual maximum discharge values. Corresponding hydrograph volumes and durations were considered. Different bivariate copulas from three families were applied and compared using different statistical, graphical and upper tail dependence tests. The parameters of the copulas were estimated using the method of moments with the inversion of Kendall's tau. The Gumbel–Hougaard copula was selected as the most appropriate for the pair of peak discharge and hydrograph volume (Q‐V). The same copula was also selected for the pair hydrograph volume and duration (V‐D), and the Student‐t copula was selected for the pair of peak discharge and hydrograph duration (Q‐D). The differences among most of the applied copulas were not significant. Different primary, secondary and conditional return periods were calculated and compared, and some relationships among them were obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

The hydrology of inland valleys in the sub‐humid zone of West Africa: rainfall‐runoff processes in the M'bé experimental watershed

Inland valleys with wet lowlands are an important water source for farming communities in the sub‐humid zone of West Africa. An inland valley and surrounding contributing watershed area located in the sub‐humid zone near M'bé in central Côte d'Ivoire was instrumented to study surface runoff and base flow mechanisms. Four flumes at different distances down the main stream and more than 100 piezometers were installed. Measurements were taken during two rainfall seasons in 1998 and 1999. Under initial wet conditions, a typical single‐peak hydrograph was observed. Under low antecedent moisture conditions, however, runoff was characterized by a double‐peaked hydrograph. The first peak, which occurred during the storm, was caused by rain falling on the saturated valley bottom. The second peak was delayed by minutes to hours from the first peak and consisted of rain flowing via the subsurface of the hydromorphic zone that surrounds the valley bottom. The duration of the delay was a function of the water table depth in the hydromorphic zone before the storm. The volume of the second peak constituted the largest portion of the stream flow. Copyright © 2003 John Wiley & Sons, Ltd.     

A simulation experiment for optimal design hyetograph selection

The aim of this work is to assess the accuracy of literature design hyetographs for the evaluation of peak discharges during flood events. Five design hyetographs are examined in a set of simulations, based upon the following steps: (i) an ideal river basin is defined, characterized by a Beta distribution shaped unit hydrograph (UH); (ii) 1000 years of synthetic rainfall are artificially generated; (iii) a discharge time‐series is obtained from the convolution of the rainfall time‐series and the UH, and the reference T‐years flood is computed from this series; (iv) for the same return period T, the parameters of the intensity–duration–frequency (IDF) curve are estimated from the 1000 years of synthetic rainfall; (v) five design hyetographs are determined from the IDF curves and are convolved with the discrete UH to find the corresponding design hydrographs; (vi) the hydrograph peaks are compared with the reference T‐years flood and the advantages and drawbacks of each of the five approaches are evaluated. The rainfall and UH parameters are varied, and the whole procedure is repeated to assess the sensitivity of results to the system configuration. We found that all design hyetographs produce flood peak estimates that are consistently biased in most of the climatic and hydrologic conditions considered. In particular, significant underestimation of the design flood results from the adoption of any rectangular hyetograph used in the context of the rational formula. In contrast, the Chicago hyetograph tends to overestimate peak flows. In two cases it is sufficient to multiply the result by a constant scaling factor to obtain robust and nearly unbiased estimates of the design floods. Copyright © 2007 John Wiley & Sons, Ltd.     

Hydrograph responses to geomorphic model watershed characteristics and precipitation variables

The primary objective of the Watershed Model Studies Project, reported herein, was to ascertain the effect of selected watershed characteristics on hydrograph parameters under a rainfall simulator. Since most of the runoff contributing to the peak flow was found to emanate from the lower half of the drainage, a measure of watershed eccentricity utilizing easily measured properties in that area is derived and evaluated as a reliable predictor of peak magnitude. In the process of isolating watershed shape, slope, size, drainage pattern, and soil depth were isolated and, along with rainfall intensity, direction of storm movement, and antecedent moisture conditions, evaluated for the models. Studies were made into the similarities between the models and real world watersheds. Three of the several conclusions are 1) the models exhibit hydrologic responses similar to those of a wide range of real watersheds; 2) watershed shape, of itself, does not have a tremendous effect on peak magnitude, and 3) watershed eccentricity is an effective, easily measured, meaningful, and useful expression of watershed shape insofar as that characteristic affects maximum peak flows and certain time parameters of the hydrograph.     

Stormflow generation and flowpath characteristics in an Amazonian rainforest catchment

The Amazon basin covers an area of roughly 7 × 10⁶ km² and encompasses diverse soil – landscape types with potentially differing hydrological behaviour. This study was conducted in the Ultisol landscape of the western Amazon basin in Peru. Processes of stormflow generation were investigated on an event basis in a first‐order rainforest catchment to establish a causal link between soil physical and precipitation characteristics, hillslope flowpaths and stormflow hydrograph attributes. A sharp decrease in soil hydraulic conductivity with depth and high rainfall intensity and frequency favour rapid near‐surface flowpaths, mainly in the form of saturation‐excess overland flow and return flow. The latter results in an almost random occurrence of overland flow, with no obvious topographic control. Hillslope flowpaths do not vary much with respect to the hydrograph attributes time of rise, response time, lag time and centroid lag time. They have the same response time as streamflow, but a somewhat lower time of rise and significantly shorter lag times. The recession constant for hillslope hydrographs is about 10 min, in contrast to the streamflow recession constants of 28, 75 and 149 min. Stormflow generation in this Ultisol rainforest catchment differs strongly from that reported for Oxisol rainforest catchments. These two soilscapes may define a spectrum of possible catchment hydrological behaviour in the Amazon basin. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of uncertainty in Digital Surface Models on the extent of inundated areas

The impact of uncertainty in ground elevation on the extent of areas that are inundated due to flooding is investigated. Land surface is represented through a Digital Surface Model (DSM). The effect of uncertainty in DSM is compared to that of the uncertainty due to rainfall. The Monte Carlo method is used to quantify the uncertainty. A typical photogrammetric procedure and conventional maps are used to obtain a reference DSM, later altered to provide DSMs of lower accuracy. Also, data from the Shuttle Radar Topography Mission are used. Floods are simulated in two stages. In the first stage, flood hydrographs for typical return periods are synthesized using generated storm hyetographs, the Soil Conservation Service–Curve Number method for effective rainfall, and the Soil Conservation Service synthetic unit hydrograph. In the second stage, hydrographs are routed via a one‐dimensional hydraulic model. Uncertainty in DSM is considered only in the second stage. Data from two real‐world basins in Greece are used. To characterize the inundated area, we employ the 90% quantile of the inundation extent and inundation topwidth for peak water level at specific river cross‐sections. For topwidths, apart from point estimates, also interval estimates are acquired using the bootstrap method. The effect of DSM uncertainty is compared to that for rainfall. Low uncertainty in DSM is found to widen the inundated area; whereas, the opposite occurred with high uncertainty. SRTM data proved unsuitable for our test basins and modelling context.     

The errors in surface runoff prediction by neglecting the relationship between infiltration rate and overland flow depth

Many simplifications are used in modeling surface runoff over a uniform slope. A very common simplification is to determine the infiltration rate independent of the overland flow depth and to combine it afterward with the kinematic-wave equation to determine the overland flow depth. Another simplication is to replace the spatially variable infiltration rates along the slope i(x, t) due to the water depth variations h(x,t) with an infiltration rate that is determined at a certain location along the slope. The aim of this study is to evaluate the errors induced by these simplications on predicted infiltration rates, overland flow depths, and total runoff volume. The error analysis is accomplished by comparing a simplified model with a model where the interaction between the overland flow depth and infiltration rate is counted. In this model, the infiltration rate is assumed to vary along the slope with the overland flow depth, even for homogeneous soil profiles. The kinematic-wave equation with interactive infiltration rate, calculated along the slopy by Richard's equation, are then solved by a finite difference scheme for a 100-m-long uniform slope. In the first error analysis, we study the effect of combining an ‘exact’ and ‘approximate’ one-dimensional infiltration rate with the kinematic-wave equation for three different soil surface roughness coefficients. The terms ‘exact’ and ‘approximate’ stand for the solution of Richard's equation with and without using the overland flow depth in the boundary condition, respectively. The simulations showed that higher infiltration rates and lower overland flow depths are obtained during the rising stage of the hydrograph when overland flow depth is used in the upper boundary condition of the one-dimensional Richard's equation. During the recession period, the simplified model predicts lower infiltration rates and higher overland flow depths. The absolute relative errors between the ‘exact’ and ‘approximate’ solutions are positively correlated to the overland flow depths which increase with the soil surface roughness coefficient. For this error analysis, the relative errors in surface runoff volume per unit slope width throughout the storm are much smaller than the relative errors in momentary overland flow depths and discharges due to the alternate signs of the deviations along the rising and falling stages. In the second error analysis, when the spatially variable infiltration rate along the slope i(x, t) is replaced in the kinematic-wave equation by i(t), calculated at the slope outlet, the overland flow depth is underestimated during the rising stage of the hydrograph and overestimated during the falling stage. The deviations during the rising stage are much smaller than the deviations during the falling stage, but they are of a longer duration. This occurs because the solution with i(x, t) recognizes that part of the slope becomes dry after rainfall stops, while overland flow still exists with i(t) determined at the slope outlet. As obtained for the first error analysis, the relative errors in surface runoff volume per unit slope width are also much smaller than the relative errors in momentary overland flow depths and discharges. The relation between the errors in overland flow depth and discharge to different mathematical simplifications enables to evaluate whether certain simplifications are justified or more computational efforts should be used.     

Propagation of uncertainties in interpolated rainfields to runoff errors

Conditional daily rainfields were generated using collocated raingauge radar data by a kriging interpolation method, and disaggregated into hourly rainfields using variants of the method of fragments. A geographic information system (GIS)-based distributed rainfall–runoff model was used to convert the hourly rainfields into hydrographs. Using the complete radar rainfall as input, the rainfall–runoff model was calibrated based on storm events taken from nested catchments. Performance statistics were estimated by comparing the observed and the complete radar rainfall simulated hydrographs. Degradation in the hydrograph performance statistics by the simulated hourly rainfields was used to identify runoff error propagation. Uncertainty in daily rainfall amounts alone caused higher errors in runoff (depth, peak, and time to peak) than those caused by uncertainties in the hourly proportions alone. However, the degradation, which reduced with runoff depth, caused by the combined uncertainties was not significantly different from that caused by the uncertainty of amounts alone.     

Hydrograph characteristics of quick and slow runoffs of a watershed outlet,Taiwan

This study explores the hydrograph characteristics of quick and slow runoffs in watershed outlet hydrographs. The quick and slow runoffs were modelled using a conceptual model of three linear cascade reservoirs that have exponential decay response expressions. Mean rainfall for model inputs was estimated using the block Kriging method. The 107 storms during the 1966–2008 events were classified as large, medium and small events according to the observed streamflow. The optimal hydrograph parameters for 61 rainfall‐runoff events were calibrated using the shuffled complex evolution optimal algorithm. The efficacy of the model was verified using the seven averaged parameters of three types of 46 events and was compared with three evaluation criteria resulting from the Nash model. The 61 calibrations were used to analyse and compare the characteristics of quick and slow flows in early and later periods (1966–2002 and 2003–2008). Finally, the following five conclusions were obtained: (1) The base time of a slow runoff hydrograph is the same as that of a total runoff hydrograph. (2) A quick runoff with a long period occurs when soil antecedent moisture is low and with a short period under a high value. (3) The time to peak of hydrograph components is directly proportional to peak time of a hyetograph; the time to peak of quick and slow flows is about 0·97 and 1·12 times the peak time of a hyetograph, respectively. (4) The peak of hydrograph components is relative to a total runoff hydrograph; the percentages for quick runoff are approximately 71% and 13% for slow flow. Finally, (5) the volume of a quick runoff component is 49% of a total runoff volume and 37% for a slow runoff volume. Copyright © 2010 John Wiley & Sons, Ltd.     

The influence of elevation error on the morphometrics of channel networks extracted from DEMs and the implications for hydrological modelling

Stream network morphometrics have been used frequently in environmental applications and are embedded in several hydrological models. This is because channel network geometry partly controls the runoff response of a basin. Network indices are often measured from channels that are mapped from digital elevation models (DEMs) using automated procedures. Simulations were used in this paper to study the influence of elevation error on the reliability of estimates of several common morphometrics, including stream order, the bifurcation, length, area and slope ratios, stream magnitude, network diameter, the flood magnitude and timing parameters of the geomorphological instantaneous unit hydrograph (GIUH) and the network width function. DEMs of three UK basins, ranging from high to low relief, were used for the analyses. The findings showed that moderate elevation error (RMSE of 1·8 m) can result in significant uncertainty in DEM‐mapped network morphometrics and that this uncertainty can be expressed in complex ways. For example, estimates of the bifurcation, length and area ratios and the flood magnitude and timing parameters of the GIUH each displayed multimodal frequency distributions, i.e. two or more estimated values were highly likely. Furthermore, these preferential estimates were wide ranging relative to the ranges typically observed for these indices. The wide‐ranging estimates of the two GIUH parameters represented significant uncertainty in the shape of the unit hydrograph. Stream magnitude, network diameter and the network width function were found to be highly sensitive to elevation error because of the difficulty in mapping low‐magnitude links. Uncertainties in the width function were found to increase with distance from outlet, implying that hydrological models that use network width contain greater uncertainty in the shape of the falling limb of the hydrograph. In light of these findings, care should be exercised when interpreting the results of analyses based on DEM‐mapped stream networks. Copyright © 2007 John Wiley & Sons, Ltd.     

Application and evaluation of a snowmelt runoff model in the Tamor River basin,Eastern Himalaya using a Markov Chain Monte Carlo (MCMC) data assimilation approach

Previous studies have drawn attention to substantial hydrological changes taking place in mountainous watersheds where hydrology is dominated by cryospheric processes. Modelling is an important tool for understanding these changes but is particularly challenging in mountainous terrain owing to scarcity of ground observations and uncertainty of model parameters across space and time. This study utilizes a Markov Chain Monte Carlo data assimilation approach to examine and evaluate the performance of a conceptual, degree‐day snowmelt runoff model applied in the Tamor River basin in the eastern Nepalese Himalaya. The snowmelt runoff model is calibrated using daily streamflow from 2002 to 2006 with fairly high accuracy (average Nash–Sutcliffe metric ~0.84, annual volume bias < 3%). The Markov Chain Monte Carlo approach constrains the parameters to which the model is most sensitive (e.g. lapse rate and recession coefficient) and maximizes model fit and performance. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall compared with simulations using observed station precipitation. The average snowmelt contribution to total runoff in the Tamor River basin for the 2002–2006 period is estimated to be 29.7 ± 2.9% (which includes 4.2 ± 0.9% from snowfall that promptly melts), whereas 70.3 ± 2.6% is attributed to contributions from rainfall. On average, the elevation zone in the 4000–5500 m range contributes the most to basin runoff, averaging 56.9 ± 3.6% of all snowmelt input and 28.9 ± 1.1% of all rainfall input to runoff. Model simulated streamflow using an interpolated precipitation data set decreases the fractional contribution from rainfall versus snowmelt compared with simulations using observed station precipitation. Model experiments indicate that the hydrograph itself does not constrain estimates of snowmelt versus rainfall contributions to total outflow but that this derives from the degree‐day melting model. Lastly, we demonstrate that the data assimilation approach is useful for quantifying and reducing uncertainty related to model parameters and thus provides uncertainty bounds on snowmelt and rainfall contributions in such mountainous watersheds. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental investigation of bedload transport processes under unsteady flow conditions

Hydraulic engineering is usually based on theoretical analysis and/or numerical modelling simulation. As the dynamic behaviour of sediment movement under unsteady flow is still unclear, and field measurement is comparatively difficult during a large flood, prior investigations through flume experiments are required. A series of flume experiments, conducted using different inflow hydrographs without sediment supply from upstream, was carried out to investigate the sediment transport process under unsteady flow conditions. A series of triangular hydrographs were performed in the experiments. The results indicate that a temporal lag was found between the flow hydrograph peak and the sediment hydrograph peak because large size sand dunes lasted for a short period in the falling limb of the flow hydrograph. The temporal lag was found to be about equal to 6–15% of the flow hydrograph duration. Owing to the temporal lag, the total bedload yield in the rising period was less than that in the falling period. Furthermore, the measured total bedload yield in the unsteady flow experiments was larger than the predicted value, which was estimated by using the results obtained from the equivalent steady flow experiment. The peak bedload transport rate for unsteady flow conditions was also larger than the predicted value. The ratios of the measured to the predicted quantities mentioned above were found to be constant values for different shapes of hydrographs. It is, therefore, expected that the analytical results of sediment transport from equivalent steady flow can be a good reference for sediment transport under unsteady flow conditions. Copyright © 2004 John Wiley & Sons, Ltd.     

Development of design flood hydrographs using probability density functions

Probability density functions (PDFs) are used to fit the shape of hydrographs and have been popularly used for the development of synthetic unit hydrographs by many hydrologists. Nevertheless, modelling the shapes of continuous stream flow hydrographs, which are probabilistic in nature, is rare. In the present study, a novel approach was followed to model the shape of stream flow hydrographs using PDF and subsequently to develop design flood hydrographs for various return periods. Four continuous PDFs, namely, two parameter Beta, Weibull, Gamma and Lognormal, were employed to fit the shape of the hydrographs of 22 years at a site of Brahmani River in eastern India. The shapes of the observed and PDF fitted hydrographs were compared and root mean square errors, error of peak discharge (EQ_P) and error of time to peak (ET_P) were computed. The best‐fitted shape and scale parameters of all PDFs were subjected to frequency analysis and the quartiles corresponding to 20‐, 50‐, 100‐ and 200‐year were estimated. The estimated parameters of each return period were used to develop the flood hydrographs for 20‐, 50‐, 100‐ and 200‐year return periods. The peak discharges of the developed design flood hydrographs were compared with the design discharges estimated from the frequency analysis of 22 years of annual peak discharges at that site. Lognormal‐produced peak discharge was very close to the estimated design discharge in case of 20‐year flood hydrograph. On the other hand, peak discharge obtained using the Weibull PDF had close agreement with the estimated design discharge obtained from frequency analysis in case of 50‐, 100‐ and 200‐year return periods. The ranking of the PDFs based on estimation of peak of design flood hydrograph for 50‐, 100‐ and 200‐year return periods was found to have the following order: Weibull > Beta > Lognormal > Gamma. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical simulation of laboratory experiments in detention pond routing with long rainfall duration

This paper establishes a numerical detention pond volume model based on the hydrological continuity equation and the Runge-Kutta numerical method. Experiments for the conditions of both steady and unsteady flow have been used to verify the model. In unsteady flow cases, the outflow hydrograph by numerical simulation are fairly consistent with experimental value. Both experimental and numerical results indicate that wider rectangular sharp-crested weirs or larger rectangular slot tend to induce greater outflow discharges, which undesirably cut down the detention volume. Experiments show that the necessary detention volume of rectangular slot is smaller than that of the rectangular sharp-crested weir for a constant flood peak reduction. That is, the rectangular slot is the recommended outflow device when flood peak reduction is the design criteria. The study also shows that necessary detention volume of the short rainfall duration is less than that of the long rainfall duration under constant allowable maximum discharge.     

Modeling risk analysis for forecasting peak discharge during flooding prevention and warning operation

This work proposes a risk analysis model to evaluate the risk of underestimating the predicted peak discharge, i.e. the exceedance of probability due to the uncertainties in rainfall information (rainfall depth, duration, and storm pattern) and the parameters of the rainfall-runoff model (Sacramento Soil Moisture Accounting model, SAC-SMA) during the flooding prevention and warning operation. The proposed risk analysis model is combined with the multivariate Monte Carlo simulation method and the Advance First-Order Second-Moment method (AFOSM). The observed rainfall and discharge measured at Yu-feng Basin study area in Shihmen reservoir watershed is used in the model development and application. The results of the model application indicate that the proposed risk analysis model can analyze the sensitivity of the uncertainty factors for the predicted peak discharge and evaluates the variation of the probability of exceeding the predicted peak discharge with respect to the rainfall depth and storm duration. In addition, the result of risk analysis for a real rainstorm event, Typhoon Morakot, shows that the proposed model successfully explores the risk of underestimating the predicted peak discharge using SAC-SMA and forecasted rainfall information and provides a probabilistic forecast of the peak discharge.     

Reliability assessment of water structures subject to data scarcity using the SCS-CN model

ABSTRACT

When discharge measurements are not available, design of water structures relies on using frequency analysis of rainfall data and applying a rainfall–runoff model to estimate a hydrograph. The Soil Conservation Service (SCS) method estimates the design hydrograph first through a rainfall–runoff transformation and next by propagating runoff to the basin outlet via the SCS unit hydrograph (UH) method. The method uses two parameters, the Curve Number (CN) and the time of concentration (T_c). However, in data-scarce areas, the calibration of CN and T_c from nearby gauged watersheds is limited and subject to high uncertainties. Therefore, the inherent uncertainty/variability of the SCS parameters may have considerable ramifications on the safety of design. In this research, a reliability approach is used to evaluate the impact of incorporating the uncertainty of CN and T_c in flood design. The sensitivity of the probabilistic outcome against the uncertainty of input parameters is calculated using the First Order Reliability Method (FORM). The results of FORM are compared with the conventional SCS results, taking solely the uncertainty of the rainfall event. The relative importance of the uncertainty of the SCS parameters is also estimated. It is found that the conventional approach, used by many practitioners, might grossly underestimate the risk of failure of water structures, due to neglecting the probabilistic nature of the SCS parameters and especially the Curve Number. The most predominant factors against which the SCS-CN method is highly uncertain are when the average rainfall value is low (less than 20 mm) or its coefficient of variation is not significant (less than 0.5), i.e. when the resulting rainfall at the design return period is low. A case study is presented for Egypt using rainfall data and CN values driven from satellite information, to determine the regions of acceptance of the SCS-CN method.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR A. Efstratiadis     

基于二次重现期的多变量洪水风险评估

由于洪水是一种具有多个特征属性的随机事件,频率分析成为洪水风险评估的一种有效手段,多变量重现期与设计值的定义与计算则是洪水频率分析中的重点和难点.本文通过构造洪水历时、洪峰与洪量的联合分布,介绍了一种新的多变量重现期定义——二次重现期,并探讨了"或"重现期、"且"重现期和二次重现期对安全与危险域识别的差异性,以及在洪水风险管理与工程设计中的合理性与可靠性.传统的"或"和"且"多变量重现期对安全与危险域的识别存在局限性,利用Kendall函数定义的二次重现期则提供了更加合理的安全与风险域识别,避免了对安全事件与危险事件的错误判定,更有利于指导洪水风险的管理.在给定的二次重现期条件下,依据出现概率最大原则推算的历时、洪峰与洪量设计值组合可以满足工程设计以较低成本承受较大风险的追求,相比于单变量设计值,考虑了洪水多个属性联合特征的多变量设计值提供了更加全面和可靠的参考信息.     

Hybrid method to update the design flood shape for spillway operation in a dam: case study of the Huites Dam,Mexico

To design and review the operation of spillways, it is necessary to estimate design hydrographs, considering their peak flow, shape and volume. A hybrid method is proposed that combines the shape of the design hydrograph obtained with the UNAM Institute of Engineering Method (UNAMIIM) with the peak flow and volume calculated from a bivariate method. This hybrid method is applied to historical data of the Huites Dam, Sinaloa, Mexico. The goal is to estimate return periods for the maximum discharge flows (that account for the damage caused downstream) and the maximum levels reached in the dam (measure of the hydrological dam safety) corresponding to a given spillway and its management policy. Therefore, to validate the method, the results obtained by the flood routing of the 50-year hydrograph are compared with those obtained by the flood routing of the three largest historical floods. Both maximum flow and elevation were in the range of values observed within 37.5–75 years corresponding to the length of the historical record.     

Soil erosion and conservation on land cultivated and drained for afforestation

Erosion of soil from pre-afforestation plough furrows has been measured on four soil types in Scotland for 12 to 18 month periods between 1987 and 1990. Rainfall-run-off was also measured at one site. Run-off is directly proportional to furrow length and rainfall intensity, and for a wide range of intensities (typically > 6 mm hr^?1) small amount of soil is flushed out of the furrows. However, for furrow spacings of 3.8 m, a critical downslope run-off increment associated with significant soil loss is of the order of 25 cm³ s^?1 m^?1, which is in accord with a storm of five years return period and a maximum intensity of 25 mm hr^?1. The total run-off volume for any hydrograph is commensurate with the total rainfall in the rainstorm — typically 40–80% by the hydrograph peak and approaching 100% by the end of the hydrograph; i.e. long term storage is negligible. A positive relationship was recorded between furrow length, slope angle and sediment yield, with deposition predominating in furrows less than 30 m in length on slopes less than a few degrees. Soil loss is proportional to the excess streampower expended by the run-off with an exponent in the range 1–1.5. For the soils examined, significant differences in soil loss when comparing sites for low power expenditure become undifferentiated at high power expenditures. For the rainfall regimes monitored, maximum soil losses were in the region of 40 kg per meter run-length of furrow, when soil peds were ripped from the bed. Laboratory data concerning the critical erosion threshold power and shear stress to erode soil peds are in general accord with the threshold furrow run-lengths defined using the field data for a five year storm and the soil losses observed.